The dynamics of a four-step feedback procedure to control chaos.

In this paper, we describe the dynamics of a four-step procedure to control the dynamics of the logistic map f(x)=μx(1-x). First, we calculate topological entropy with given accuracy through massive computations. Second, we find the parameter regions where the model has complicated dynamical behavior. Finally, to avoid undesirable dynamics, our computations also show that we should take into account Parrondo's paradox "simple+simple=complex."